Question: Solve for $x$ and $y$ using elimination. ${6x+2y = 14}$ ${5x-2y = 8}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $11x = 22$ $\dfrac{11x}{{11}} = \dfrac{22}{{11}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {6x+2y = 14}\thinspace$ to find $y$ ${6}{(2)}{ + 2y = 14}$ $12+2y = 14$ $12{-12} + 2y = 14{-12}$ $2y = 2$ $\dfrac{2y}{{2}} = \dfrac{2}{{2}}$ ${y = 1}$ You can also plug ${x = 2}$ into $\thinspace {5x-2y = 8}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ - 2y = 8}$ ${y = 1}$